html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.4827.01

 Input Form

 Integrate[z^n E^(b Sqrt[z] + d z + e) Sinh[a Sqrt[z] + p z + q] Cosh[c Sqrt[z] + f z + g]^v, z] == I 2^(-2 - 2 n - v) Binomial[v, v/2] (1 - Mod[v, 2]) (E^(e - (-a + b)^2/(4 (d - p)) + (I Pi)/2 - q) (d - p)^(-2 - 2 n) Sum[(-1)^(-h + i) 4^i (-a + b)^(-h - i + 2 n) (-a + b + 2 (d - p) Sqrt[z])^(h + i) (-((-a + b + 2 (d - p) Sqrt[z])^2/(d - p)))^((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((-a + b) (-a + b + 2 (d - p) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((-a + b + 2 (d - p) Sqrt[z])^2/ (4 (d - p)))] + 2 (d - p) Sqrt[-((-a + b + 2 (d - p) Sqrt[z])^2/ (d - p))] Gamma[(1/2) (2 + h + i), -((-a + b + 2 (d - p) Sqrt[z])^2/(4 (d - p)))]), {i, 0, n}, {h, 0, i}] + E^(e - (a + b)^2/(4 (d + p)) - (I Pi)/2 + q) (d + p)^(-2 - 2 n) Sum[(-1)^(-h + i) 4^i (a + b)^(-h - i + 2 n) (a + b + 2 (d + p) Sqrt[z])^(h + i) (-((a + b + 2 (d + p) Sqrt[z])^2/(d + p)))^((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((a + b) (a + b + 2 (d + p) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((a + b + 2 (d + p) Sqrt[z])^2/ (4 (d + p)))] + 2 (d + p) Sqrt[-((a + b + 2 (d + p) Sqrt[z])^2/ (d + p))] Gamma[(1/2) (2 + h + i), -((a + b + 2 (d + p) Sqrt[z])^2/(4 (d + p)))]), {i, 0, n}, {h, 0, i}]) + I 2^(-2 - 2 n - v) Sum[Binomial[v, s] (E^(e + (I Pi)/2 - q - (-a + b + c (2 s - v))^2/ (4 (d - p + f (2 s - v))) + g (2 s - v)) (d - p + f (2 s - v))^ (-2 - 2 n) Sum[(-1)^(-h + i) 4^i (-a + b + c (2 s - v))^ (-h - i + 2 n) (-a + b + c (2 s - v) + 2 (d - p + f (2 s - v)) Sqrt[z])^(h + i) (-((-a + b + c (2 s - v) + 2 (d - p + f (2 s - v)) Sqrt[z])^2/(d - p + f (2 s - v))))^ ((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((-a + b + c (2 s - v)) (-a + b + c (2 s - v) + 2 (d - p + f (2 s - v)) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((-a + b + c (2 s - v) + 2 (d - p + f (2 s - v)) Sqrt[z])^2/(4 (d - p + f (2 s - v))))] + 2 (d - p + f (2 s - v)) Sqrt[-((-a + b + c (2 s - v) + 2 (d - p + f (2 s - v)) Sqrt[z])^ 2/(d - p + f (2 s - v)))] Gamma[(1/2) (2 + h + i), -((-a + b + c (2 s - v) + 2 (d - p + f (2 s - v)) Sqrt[z])^2/(4 (d - p + f (2 s - v))))]), {i, 0, n}, {h, 0, i}] + E^(e - (I Pi)/2 + q - (a + b + c (2 s - v))^2/ (4 (d + p + f (2 s - v))) + g (2 s - v)) (d + p + f (2 s - v))^ (-2 - 2 n) Sum[(-1)^(-h + i) 4^i (a + b + c (2 s - v))^ (-h - i + 2 n) (a + b + c (2 s - v) + 2 (d + p + f (2 s - v)) Sqrt[z])^(h + i) (-((a + b + c (2 s - v) + 2 (d + p + f (2 s - v)) Sqrt[z])^2/(d + p + f (2 s - v))))^ ((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((a + b + c (2 s - v)) (a + b + c (2 s - v) + 2 (d + p + f (2 s - v)) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((a + b + c (2 s - v) + 2 (d + p + f (2 s - v)) Sqrt[z])^2/(4 (d + p + f (2 s - v))))] + 2 (d + p + f (2 s - v)) Sqrt[-((a + b + c (2 s - v) + 2 (d + p + f (2 s - v)) Sqrt[z])^2/( d + p + f (2 s - v)))] Gamma[(1/2) (2 + h + i), -((a + b + c (2 s - v) + 2 (d + p + f (2 s - v)) Sqrt[z])^2/(4 (d + p + f (2 s - v))))]), {i, 0, n}, {h, 0, i}] + E^(e + (I Pi)/2 - q + g (-2 s + v) - (-a + b + c (-2 s + v))^2/ (4 (d - p + f (-2 s + v)))) (d - p + f (-2 s + v))^(-2 - 2 n) Sum[(-1)^(-h + i) 4^i (-a + b + c (-2 s + v))^(-h - i + 2 n) (-a + b + c (-2 s + v) + 2 (d - p + f (-2 s + v)) Sqrt[z])^(h + i) (-((-a + b + c (-2 s + v) + 2 (d - p + f (-2 s + v)) Sqrt[z])^2/ (d - p + f (-2 s + v))))^((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((-a + b + c (-2 s + v)) (-a + b + c (-2 s + v) + 2 (d - p + f (-2 s + v)) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((-a + b + c (-2 s + v) + 2 (d - p + f (-2 s + v)) Sqrt[z])^2/( 4 (d - p + f (-2 s + v))))] + 2 (d - p + f (-2 s + v)) Sqrt[-((-a + b + c (-2 s + v) + 2 (d - p + f (-2 s + v)) Sqrt[z])^ 2/(d - p + f (-2 s + v)))] Gamma[(1/2) (2 + h + i), -((-a + b + c (-2 s + v) + 2 (d - p + f (-2 s + v)) Sqrt[z])^2/( 4 (d - p + f (-2 s + v))))]), {i, 0, n}, {h, 0, i}] + E^(e - (I Pi)/2 + q + g (-2 s + v) - (a + b + c (-2 s + v))^2/ (4 (d + p + f (-2 s + v)))) (d + p + f (-2 s + v))^(-2 - 2 n) Sum[(-1)^(-h + i) 4^i (a + b + c (-2 s + v))^(-h - i + 2 n) (a + b + c (-2 s + v) + 2 (d + p + f (-2 s + v)) Sqrt[z])^(h + i) (-((a + b + c (-2 s + v) + 2 (d + p + f (-2 s + v)) Sqrt[z])^2/ (d + p + f (-2 s + v))))^((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((a + b + c (-2 s + v)) (a + b + c (-2 s + v) + 2 (d + p + f (-2 s + v)) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((a + b + c (-2 s + v) + 2 (d + p + f (-2 s + v)) Sqrt[z])^2/(4 (d + p + f (-2 s + v))))] + 2 (d + p + f (-2 s + v)) Sqrt[-((a + b + c (-2 s + v) + 2 (d + p + f (-2 s + v)) Sqrt[z])^ 2/(d + p + f (-2 s + v)))] Gamma[(1/2) (2 + h + i), -((a + b + c (-2 s + v) + 2 (d + p + f (-2 s + v)) Sqrt[z])^2/(4 (d + p + f (-2 s + v))))]), {i, 0, n}, {h, 0, i}]), {s, 0, Floor[(1/2) (-1 + v)]}] /; Element[n, Integers] && n >= 0 && Element[v, Integers] && v > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "n"], SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]], "+", "e"]]], RowBox[List["Sinh", "[", RowBox[List[RowBox[List["a", " ", SqrtBox["z"]]], "+", RowBox[List["p", " ", "z"]], "+", "q"]], "]"]], SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], "v"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]], "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]]]]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "p"]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]]]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "p"]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]]]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]], "-", "v"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "-", "q", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]]]]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["\[Sqrt]", RowBox[List["(", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]]]]]], ")"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "+", "q", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]]]]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "-", "q", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]], ")"]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["\[Sqrt]", RowBox[List["(", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]], ")"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]], ")"]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "+", "q", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]], ")"]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["\[Sqrt]", RowBox[List["(", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]], ")"]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]], ")"]]]]]]]], "]"]]]]]], ")"]]]]]]]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 z n z b + d z + e sinh ( z a + p z + q ) cosh v ( z c + f z + g ) z 2 - 2 n - v - 2 ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - v mod 2 \$CellContext`v 2 ) ( - ( b - a ) 2 4 ( d - p ) + e - q + π 2 ( d - p ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( b - a ) - h - i + 2 n ( - a + b + 2 ( d - p ) z ) h + i ( - ( - a + b + 2 ( d - p ) z ) 2 d - p ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( b - a ) ( - a + b + 2 ( d - p ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( - a + b + 2 ( d - p ) z ) 2 4 ( d - p ) ) + 2 - ( - a + b + 2 ( d - p ) z ) 2 d - p ( d - p ) Γ ( 1 2 ( h + i + 2 ) , - ( - a + b + 2 ( d - p ) z ) 2 4 ( d - p ) ) ) + - ( a + b ) 2 4 ( d + p ) + e + q - π 2 ( d + p ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( a + b ) - h - i + 2 n ( a + b + 2 ( d + p ) z ) h + i ( - ( a + b + 2 ( d + p ) z ) 2 d + p ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( a + b ) ( a + b + 2 ( d + p ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( a + b + 2 ( d + p ) z ) 2 4 ( d + p ) ) + 2 - ( a + b + 2 ( d + p ) z ) 2 d + p ( d + p ) Γ ( 1 2 ( h + i + 2 ) , - ( a + b + 2 ( d + p ) z ) 2 4 ( d + p ) ) ) ) + 2 - 2 n - v - 2 s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( - a + b + c ( 2 s - v ) ) 2 4 ( d - p + f ( 2 s - v ) ) + e - q + g ( 2 s - v ) + π 2 ( d - p + f ( 2 s - v ) ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( - a + b + c ( 2 s - v ) ) - h - i + 2 n ( - a + b + c ( 2 s - v ) + 2 ( d - p + f ( 2 s - v ) ) z ) h + i ( - ( - a + b + c ( 2 s - v ) + 2 ( d - p + f ( 2 s - v ) ) z ) 2 d - p + f ( 2 s - v ) ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( - a + b + c ( 2 s - v ) ) ( - a + b + c ( 2 s - v ) + 2 ( d - p + f ( 2 s - v ) ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( - a + b + c ( 2 s - v ) + 2 ( d - p + f ( 2 s - v ) ) z ) 2 4 ( d - p + f ( 2 s - v ) ) ) + 2 ( d - p + f ( 2 s - v ) ) Γ ( 1 2 ( h + i + 2 ) , - ( - a + b + c ( 2 s - v ) + 2 ( d - p + f ( 2 s - v ) ) z ) 2 4 ( d - p + f ( 2 s - v ) ) ) - ( - a + b + c ( 2 s - v ) + 2 ( d - p + f ( 2 s - v ) ) z ) 2 d - p + f ( 2 s - v ) ) + - ( a + b + c ( 2 s - v ) ) 2 4 ( d + p + f ( 2 s - v ) ) + e + q + g ( 2 s - v ) - π 2 ( d + p + f ( 2 s - v ) ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( a + b + c ( 2 s - v ) ) - h - i + 2 n ( a + b + c ( 2 s - v ) + 2 ( d + p + f ( 2 s - v ) ) z ) h + i ( - ( a + b + c ( 2 s - v ) + 2 ( d + p + f ( 2 s - v ) ) z ) 2 d + p + f ( 2 s - v ) ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( a + b + c ( 2 s - v ) ) ( a + b + c ( 2 s - v ) + 2 ( d + p + f ( 2 s - v ) ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( a + b + c ( 2 s - v ) + 2 ( d + p + f ( 2 s - v ) ) z ) 2 4 ( d + p + f ( 2 s - v ) ) ) + 2 - ( a + b + c ( 2 s - v ) + 2 ( d + p + f ( 2 s - v ) ) z ) 2 d + p + f ( 2 s - v ) ( d + p + f ( 2 s - v ) ) Γ ( 1 2 ( h + i + 2 ) , - ( a + b + c ( 2 s - v ) + 2 ( d + p + f ( 2 s - v ) ) z ) 2 4 ( d + p + f ( 2 s - v ) ) ) ) + - ( - a + b + c ( v - 2 s ) ) 2 4 ( d - p + f ( v - 2 s ) ) + e - q + g ( v - 2 s ) + π 2 ( d - p + f ( v - 2 s ) ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( - a + b + c ( v - 2 s ) ) - h - i + 2 n ( - a + b + c ( v - 2 s ) + 2 ( d - p + f ( v - 2 s ) ) z ) h + i ( - ( - a + b + c ( v - 2 s ) + 2 ( d - p + f ( v - 2 s ) ) z ) 2 d - p + f ( v - 2 s ) ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( - a + b + c ( v - 2 s ) ) ( - a + b + c ( v - 2 s ) + 2 ( d - p + f ( v - 2 s ) ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( - a + b + c ( v - 2 s ) + 2 ( d - p + f ( v - 2 s ) ) z ) 2 4 ( d - p + f ( v - 2 s ) ) ) + 2 ( d - p + f ( v - 2 s ) ) Γ ( 1 2 ( h + i + 2 ) , - ( - a + b + c ( v - 2 s ) + 2 ( d - p + f ( v - 2 s ) ) z ) 2 4 ( d - p + f ( v - 2 s ) ) ) - ( - a + b + c ( v - 2 s ) + 2 ( d - p + f ( v - 2 s ) ) z ) 2 d - p + f ( v - 2 s ) ) + - ( a + b + c ( v - 2 s ) ) 2 4 ( d + p + f ( v - 2 s ) ) + e + q + g ( v - 2 s ) - π 2 ( d + p + f ( v - 2 s ) ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( a + b + c ( v - 2 s ) ) - h - i + 2 n ( a + b + c ( v - 2 s ) + 2 ( d + p + f ( v - 2 s ) ) z ) h + i ( - ( a + b + c ( v - 2 s ) + 2 ( d + p + f ( v - 2 s ) ) z ) 2 d + p + f ( v - 2 s ) ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( a + b + c ( v - 2 s ) ) ( a + b + c ( v - 2 s ) + 2 ( d + p + f ( v - 2 s ) ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( a + b + c ( v - 2 s ) + 2 ( d + p + f ( v - 2 s ) ) z ) 2 4 ( d + p + f ( v - 2 s ) ) ) + 2 ( d + p + f ( v - 2 s ) ) Γ ( 1 2 ( h + i + 2 ) , - ( a + b + c ( v - 2 s ) + 2 ( d + p + f ( v - 2 s ) ) z ) 2 4 ( d + p + f ( v - 2 s ) ) ) - ( a + b + c ( v - 2 s ) + 2 ( d + p + f ( v - 2 s ) ) z ) 2 d + p + f ( v - 2 s ) ) ) /; n v + Condition z z n z 1 2 b d z e z 1 2 a p z q z 1 2 c f z g v 2 -2 n -1 v -2 Binomial v v 2 -1 1 -1 \$CellContext`v 2 -1 b -1 a 2 4 d -1 p -1 e -1 q 2 -1 d -1 p -2 n -2 h 0 i i 0 n -1 i -1 h 4 i b -1 a -1 h -1 i 2 n -1 a b 2 d -1 p z 1 2 h i -1 -1 a b 2 d -1 p z 1 2 2 d -1 p -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i b -1 a -1 a b 2 d -1 p z 1 2 Gamma 1 2 h i 1 -1 -1 a b 2 d -1 p z 1 2 2 4 d -1 p -1 2 -1 -1 a b 2 d -1 p z 1 2 2 d -1 p -1 1 2 d -1 p Gamma 1 2 h i 2 -1 -1 a b 2 d -1 p z 1 2 2 4 d -1 p -1 -1 a b 2 4 d p -1 e q -1 2 -1 d p -2 n -2 h 0 i i 0 n -1 i -1 h 4 i a b -1 h -1 i 2 n a b 2 d p z 1 2 h i -1 a b 2 d p z 1 2 2 d p -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i a b a b 2 d p z 1 2 Gamma 1 2 h i 1 -1 a b 2 d p z 1 2 2 4 d p -1 2 -1 a b 2 d p z 1 2 2 d p -1 1 2 d p Gamma 1 2 h i 2 -1 a b 2 d p z 1 2 2 4 d p -1 2 -2 n -1 v -2 s 0 v -1 2 -1 Binomial v s -1 -1 a b c 2 s -1 v 2 4 d -1 p f 2 s -1 v -1 e -1 q g 2 s -1 v 2 -1 d -1 p f 2 s -1 v -2 n -2 h 0 i i 0 n -1 i -1 h 4 i -1 a b c 2 s -1 v -1 h -1 i 2 n -1 a b c 2 s -1 v 2 d -1 p f 2 s -1 v z 1 2 h i -1 -1 a b c 2 s -1 v 2 d -1 p f 2 s -1 v z 1 2 2 d -1 p f 2 s -1 v -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i -1 a b c 2 s -1 v -1 a b c 2 s -1 v 2 d -1 p f 2 s -1 v z 1 2 Gamma 1 2 h i 1 -1 -1 a b c 2 s -1 v 2 d -1 p f 2 s -1 v z 1 2 2 4 d -1 p f 2 s -1 v -1 2 d -1 p f 2 s -1 v Gamma 1 2 h i 2 -1 -1 a b c 2 s -1 v 2 d -1 p f 2 s -1 v z 1 2 2 4 d -1 p f 2 s -1 v -1 -1 -1 a b c 2 s -1 v 2 d -1 p f 2 s -1 v z 1 2 2 d -1 p f 2 s -1 v -1 1 2 -1 a b c 2 s -1 v 2 4 d p f 2 s -1 v -1 e q g 2 s -1 v -1 2 -1 d p f 2 s -1 v -2 n -2 h 0 i i 0 n -1 i -1 h 4 i a b c 2 s -1 v -1 h -1 i 2 n a b c 2 s -1 v 2 d p f 2 s -1 v z 1 2 h i -1 a b c 2 s -1 v 2 d p f 2 s -1 v z 1 2 2 d p f 2 s -1 v -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i a b c 2 s -1 v a b c 2 s -1 v 2 d p f 2 s -1 v z 1 2 Gamma 1 2 h i 1 -1 a b c 2 s -1 v 2 d p f 2 s -1 v z 1 2 2 4 d p f 2 s -1 v -1 2 -1 a b c 2 s -1 v 2 d p f 2 s -1 v z 1 2 2 d p f 2 s -1 v -1 1 2 d p f 2 s -1 v Gamma 1 2 h i 2 -1 a b c 2 s -1 v 2 d p f 2 s -1 v z 1 2 2 4 d p f 2 s -1 v -1 -1 -1 a b c v -1 2 s 2 4 d -1 p f v -1 2 s -1 e -1 q g v -1 2 s 2 -1 d -1 p f v -1 2 s -2 n -2 h 0 i i 0 n -1 i -1 h 4 i -1 a b c v -1 2 s -1 h -1 i 2 n -1 a b c v -1 2 s 2 d -1 p f v -1 2 s z 1 2 h i -1 -1 a b c v -1 2 s 2 d -1 p f v -1 2 s z 1 2 2 d -1 p f v -1 2 s -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i -1 a b c v -1 2 s -1 a b c v -1 2 s 2 d -1 p f v -1 2 s z 1 2 Gamma 1 2 h i 1 -1 -1 a b c v -1 2 s 2 d -1 p f v -1 2 s z 1 2 2 4 d -1 p f v -1 2 s -1 2 d -1 p f v -1 2 s Gamma 1 2 h i 2 -1 -1 a b c v -1 2 s 2 d -1 p f v -1 2 s z 1 2 2 4 d -1 p f v -1 2 s -1 -1 -1 a b c v -1 2 s 2 d -1 p f v -1 2 s z 1 2 2 d -1 p f v -1 2 s -1 1 2 -1 a b c v -1 2 s 2 4 d p f v -1 2 s -1 e q g v -1 2 s -1 2 -1 d p f v -1 2 s -2 n -2 h 0 i i 0 n -1 i -1 h 4 i a b c v -1 2 s -1 h -1 i 2 n a b c v -1 2 s 2 d p f v -1 2 s z 1 2 h i -1 a b c v -1 2 s 2 d p f v -1 2 s z 1 2 2 d p f v -1 2 s -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i a b c v -1 2 s a b c v -1 2 s 2 d p f v -1 2 s z 1 2 Gamma 1 2 h i 1 -1 a b c v -1 2 s 2 d p f v -1 2 s z 1 2 2 4 d p f v -1 2 s -1 2 d p f v -1 2 s Gamma 1 2 h i 2 -1 a b c v -1 2 s 2 d p f v -1 2 s z 1 2 2 4 d p f v -1 2 s -1 -1 a b c v -1 2 s 2 d p f v -1 2 s z 1 2 2 d p f v -1 2 s -1 1 2 n v SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "n_"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b_", " ", SqrtBox["z_"]]], "+", RowBox[List["d_", " ", "z_"]], "+", "e_"]]], " ", RowBox[List["Sinh", "[", RowBox[List[RowBox[List["a_", " ", SqrtBox["z_"]]], "+", RowBox[List["p_", " ", "z_"]], "+", "q_"]], "]"]], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SqrtBox["z_"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]], "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]]]]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "-", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "p"]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p"]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]]]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "+", "q"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "p"]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "p"]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p"]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]]]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]], "-", "v"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "-", "q", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]]]]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "+", "q", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]]]]], "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "-", "q", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"], "+", "q", "+", RowBox[List["g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["2", " ", "n"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "0"]], "i"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["-", "h"]], "+", "i"]]], " ", SuperscriptBox["4", "i"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List[RowBox[List["-", "h"]], "-", "i", "+", RowBox[List["2", " ", "n"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], RowBox[List["h", "+", "i"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", "h", "-", "i"]], ")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["i", ",", "h"]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "i"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["2", "+", "h", "+", "i"]], ")"]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "p", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]]], "]"]]]]]], ")"]]]]]]]]]]]], ")"]]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]], "&&", RowBox[List["v", "\[Element]", "Integers"]], "&&", RowBox[List["v", ">", "0"]]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2002-12-18